Stochastic evolution equations driven by cylindrical stable noise

Tomasz Kosmala and Markus Riedle

Stochastic Processes and their Applications, 2022, vol. 149, issue C, 278-307

Abstract: We prove existence and uniqueness of a mild solution of a stochastic evolution equation driven by a standard α-stable cylindrical Lévy process defined on a Hilbert space for α∈(1,2). The coefficients are assumed to map between certain domains of fractional powers of the generator present in the equation. The solution is constructed as a weak limit of the Picard iteration using tightness arguments. Existence of strong solution is obtained by a general version of the Yamada–Watanabe theorem.

Keywords: Cylindrical Lévy processes; Stable processes; Stochastic partial differential equations; Tightness (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.03.014

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